What is the average rate of change of $g(x)=7-8x$ over the interval $[3,10]$ ?
Solution: This is the formula for the average rate of change of a function $f$ over the interval $[a,b]$ : $\dfrac{f(b)-f(a)}{b-a}$ We will need to know the values of $g(3)$ and $g(10)$ to find the slope. $\begin{aligned} g(3)&=7-8(3) \\\\ &=-17 \\\\\\ g(10)&=7-8(10) \\\\ &=-73 \\\\\\ \dfrac{g(10)-g(3)}{10-3}&=\dfrac{-73-(-17)}{7} \\\\ &=-8 \end{aligned}$ The average rate of change of $g$ over the interval $[3,10]$ is $-8$. Notice that the average rate of change is calculated just like the slope of the secant line that intersects the graph of the function at the interval's endpoints. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}10}$ ${\llap{-}20}$ ${\llap{-}30}$ ${\llap{-}40}$ ${\llap{-}50}$ ${\llap{-}60}$ ${\llap{-}70}$ ${\llap{-}80}$ ${\llap{-}90}$ $y$ $x$ $(3,g(3))$ $(10,g(10))$ secant line